In this paper, to address these limitations, we propose two new hypergraph Laplacians based on the diffusion framework that allows us to find the influential higher-order interactions in a hypergraph of any size and with any desired classical centrality measure; one is based on diffusion between fixed size hyperedges, and the other is based on diffusion between all hyperedges. The previously developed hypergraph Laplacians are only defined for special hypergraphs, and more importantly, neglect the relations between hyperedges. Thanks to the proposed Laplacians, we can model the complete relations between hyperedges of any size. Next, we redefine four graph centrality measures, namely DFF, degree, betweenness, and closeness, to hypergraphs and rank higher-order interactions based on these measures. One can also similarly redefine other classical centrality measures, but we believe working with four centralities would be enough to show the effectiveness of the proposed method. For evaluation, we experiment on several undirected real-world network datasets and evaluate the performance using the Susceptible-Infected-Recovered (SIR) simulation model[1]}. The experimental results suggest that our methods are quite promising in finding influential higher-order interactions.
